With ssh -X you get X11 forwarding, which means that you can run X11 client programs programs such as Xterm, firefox, etc that execute on your ununtu netbook, and display them on your local X11 server (the desktop you are sitting at).
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Justin DearingAug 9 '12 at 21:48

The most important thing to do to be able to access your computer inside your home network from the internet is to enable your modem/firewall to open one or more ports and direct them to your netbook.

Let's use a simple example and assume your internet connection has a static IP (if it is dynamic you need to find out when it changes and to which IP or you won't be able to access it anymore). Let's also assume you want ssh (port 22) access to your netbook.

Configure your modem/firewall to direct traffic to port 22 to your netbook at IP 10.1.2.20. The names used for this are not always the same, it could be application level gateway, firewall, application firewall, what have you. Just as long as you make sure to direct traffic the proper way.

As an aside, you could also enable DMZ and configure the DMZ to use your netbook at 10.1.2.20, however that opens up your netbook to more than just port 22 for ssh and you'd have to configure a firewall on your netbook to prevent anything bad to happen. So that's probably out of the scope of your question.

By default your netbook already should have an ssh server running, if not run:

sudo apt-get install openssh-server

Once finished the ssh server is up and running.

You should also install a tool to prevent brute force password hacking to your ssh server:

sudo apt-get install fail2ban

Read the docs in /usr/share/doc/fail2ban/ on how to enable it, it's quite easy to do.

If you set everything up correctly you should be able to log into your netbook remotely from anywhere like this: